Heat Flow Analysis for Unsaturated Soils - Unsaturated Soil Mechanics in Engineering Practice - page 487

CHAPTER 10

Heat Flow Analysis for Unsaturated Soils

10.1 INTRODUCTION possibly two) of the physical processes are dominant for a

particular geotechnical engineering problem and therefore a
rigorous solution of all processes is unwarranted.
The constitutive relations associated with heat flow are
first presented for the situation where heat flow is above the
freezing phase change isotherm (e.g., 0 ◦ C). This is followed
with a description of the constitutive relations related to
freezing and thawing. Partial differential equations are then
derived for heat flow problems of increasing complexity.
There is a section on the measurement of thermal prop-
erties followed by a section on estimation procedures for
the determination of thermal conductivity properties. The
estimation of saturated and unsaturated thermal properties
contains a summary of properties and equations that have
been published by various researchers. Tables and plots of
previously measured thermal properties are useful for esti-
mating specific thermal properties for each phase of the soil.
A number of example problems are solved using the solution
of the partial differential equation for heat flow.

Heat transfer in soils occurs by three primary mechanisms:
conduction, convection, and radiation. Heat transfer by con-
duction occurs as thermal energy is transferred between
molecules as a result of direct contact. Heat transfer by
convection occurs when kinetic energy in the pore fluid of
a soil is transported from one location to another location.
Heat transfer by convection is usually considered to be much
smaller than heat transfer by conduction (Milly, 1984a) and
can be neglected in many situations (Jame and Norum, 1980;
Wilson, 1990).
Heat transfer associated with radiation occurs as electro-
magnetic energy is emitted from one object and transmitted
through space to another object. Radiation from the sun is
the driving mechanism for phase change in the form of
vaporization and condensation at the ground surface. The
phase change may also be in the form of freezing and thaw-
ing of the water in soils. Radiation has an important role in
unsaturated soils, but it is generally considered as small in
comparison to heat flow by conduction.
Unsaturated soil mechanics problems can involve heat
transfer through each of the three mentioned mechanisms.
It is possible for the water phase in soils to exist in the
liquid phase and solid phase as well as being in the vapor
phase and condensing back to the liquid phase. This chapter
will focus primarily on unsaturated soil mechanics problems
where there is heat flow by conduction. Chapter 6 dealt with
the calculation of moisture flux in vapor form at ground sur-
face. As such, Chapter 6 describes the role of net radiation
in the calculation of evaporation and transpiration.
Many environmental problems involve the complex inter-
action of several physical processes. For example, it is com-
mon for heat fluxes, air fluxes, and vapor fluxes to occur
simultaneously in an unsaturated soil. This means that there
are several physical processes that are coupled processes.
It is difficult to model interrelated soil problems without
fully understanding the physical processes associated with
each independent process. It is often possible that one (or

10.1.1 Heat Flow Processes Involving
Unsaturated Soils
Conductive heat flow is often viewed as being somewhat
analogous to the flow of water through soil with the obvi-
ous exception that there is no gravity component in the total
energy state that drives heat flow. There are some similari-
ties between heat flow by conduction and water flow through
soils, but it is important to also understand the fundamental
differences.
Heat flow by conduction is similar to water flow in that
both processes involve two primary soil properties. One soil
property defines the rate at which flow occurs and the other
property defines the capacity for storage. In the case of heat
flow, the rate at which flow occurs is defined as the thermal
conductivity λ of the material (e.g., unsaturated soil). The
capacity to store thermal energy is defined in terms of the
volumetric heat capacity ζ of the material. Objects get warmer
as heat is stored in much the same manner that a soil gets